CRM CAMP in Nonlinear Analysis

Computer-Assisted Mathematical Proofs in Nonlinear Analysis

November 17, 2020 from 10:00 to 11:00 (Montreal/EST time) Zoom meeting

Stable periodic orbits for the Mackey-Glass equation

Seminar presented by Ferenc Bartha (University of Szeged, Hungary)

We consider the classical Mackey-Glass delay differential equation. By letting n go to infinity in the part encapsulating the delayed term, we obtain a limiting hybrid delay equation. We investigate how periodic solutions of this limiting equation are related to periodic solutions of the original MG equation for large n. Then, we establish a procedure for constructing such periodic solutions via forward time integration. Finally, we use rigorous numerics to establish the existence of stable periodic orbits for various parameters of the MG equation. We note that some of these solutions exhibit seemingly complicated dynamics, yet they are stable periodic orbits.